Whether neutron halos — dilute distributions of one or two weakly bound neutrons around a compact core — occur in nuclei heavier than 37^{37}Mg, which remains the heaviest nucleus with an experimentally established halo, is an open question at the neutron-rich frontier. A phenomenological deformed Woods-Saxon study (Hamamoto, 2017) argued that near the quenched N=50N=50 shell gap the even-ZZ odd-NN nuclei 71^{71}Cr, 73^{73}Cr, 75^{75}Cr, and 77^{77}Fe should acquire prolate deformation and host deformed ss-wave halos, with 53^{53}Ar a weaker pp- or ss-wave candidate. Later calculations that include continuum coupling, deformation, and pairing — relativistic mean field in the complex momentum representation and the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) — partially support this (75^{75}Cr is the candidate most consistently supported by later calculations), but disagree on binding and on halo status for 71,73^{71,73}Cr and 77^{77}Fe, contradict the 53^{53}Ar suggestion, and rely on unvalidated extrapolations. None of the candidate nuclei has been observed, so their separation energies, drip-line location, and halo status are unmeasured. The problem is to establish which, if any, nuclei heavier than 37^{37}Mg carry neutron halos, and with what binding windows, spin-parity, deformation, and breakup or low-energy electric-dipole signatures.

Background

A neutron halo is an extended, low-density distribution of one or two weakly bound neutrons orbiting a compact core. It forms when the valence neutron occupies an orbital with little or no centrifugal barrier (angular momentum l=0l=0 or 11) and has a one-neutron separation energy SnS_n (the energy required to remove one neutron) of only a few hundred keV. Along an isotopic chain SnS_n decreases toward the neutron drip line, the boundary beyond which nuclei are unbound to neutron emission, and odd-NN nuclei lose their last binding before the even-NN neighbors because of pairing. Halos are detected experimentally either through enlarged matter radii (from reaction cross sections) or through the soft, near-threshold electric-dipole (E1) response and Coulomb-breakup cross sections produced by the weakly bound valence neutron.

Because high-ll orbitals are protected by their centrifugal barrier, established halos were long confined to the light pp and sdsd shells. Deformation changed this picture. In a quadrupole-deformed potential the single-particle orbitals are Nilsson levels labeled by the projection Ω\Omega of the angular momentum on the symmetry axis and by the parity π\pi, and a weakly bound level with Ω=1/2\Omega=1/2 or 3/23/2 mixes low-ll components into high-jj orbits, so deformation can generate halo amplitude even where the spherical orbital would not. On this basis Coulomb-breakup measurements established a deformed pp-wave halo in 31^{31}Ne and, heavier still, in 37^{37}Mg, which is still the heaviest nucleus with an experimentally identified halo.

Hamamoto (2017) asked where the next halo heavier than 37^{37}Mg should be sought. Near the neutron drip line the spherical N=50N=50 shell gap narrows, leaving the neutron orbitals 1g9/21g_{9/2}, 3s1/23s_{1/2}, and 2d5/22d_{5/2} nearly degenerate; filling the first half of such a close-lying set drives prolate deformation by the Jahn-Teller mechanism (the energy gained by lifting an orbital near-degeneracy), and the deformed Ωπ=1/2+\Omega^\pi=1/2^+ levels descending from g9/2g_{9/2} acquire s1/2s_{1/2} components. Working in a deformed Woods-Saxon potential without pairing, restricted to prolate shapes, and using evaluated or extrapolated SnS_n values from the US National Nuclear Data Center (NNDC) evaluation, she identified the even-ZZ odd-NN nuclei 71^{71}Cr, 73^{73}Cr, 75^{75}Cr, and 77^{77}Fe (N=47,49,51,51N=47,49,51,51) as promising deformed ss-wave halo candidates, and 53^{53}Ar as a possible pp- or ss-wave halo — all conditional on these nuclei lying inside the drip line. She stated the weaknesses of the prediction explicitly: the drip-line location and true SnS_n values are unknown; pairing correlations were neglected; no reliable microscopic mean-field interaction for drip-line nuclei existed, so a fully self-consistent Hartree-Fock-Bogoliubov treatment with continuum coupling, deformation, and pairing was missing; oblate or triaxial shapes were not considered; and experimental confirmation (for example by Coulomb breakup or spectroscopy) would be required.

Subsequent work has supplied much of the missing machinery. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is a self-consistent covariant density-functional framework that couples deformation, pairing, and continuum states and now exists as a mass table covering even-ZZ nuclei to the drip lines; in that framework the N=50N=50 shell closure is indeed quenched for 21≤Z≤2721\le Z\le 27, predominantly by deformation, supporting the level-mixing picture underlying the prediction. A complementary complex-momentum-representation method — single-particle states represented on a contour in the complex momentum plane, so that unbound resonances are treated on the same footing as bound states — handles deformed systems, and calculations that are ab initio (built from internucleon forces rather than a fitted mean field) using the valence-space in-medium similarity renormalization group, which derives effective shell-model interactions from such forces, have begun to predict halo candidates in the intermediate-mass Mg-S region. Experimentally, however, the frontier has not moved past 70^{70}Cr and 76^{76}Fe, so every prediction in this region remains untested.

Problem Statement

Determine whether neutron halos occur in any nucleus heavier than 37^{37}Mg — in particular whether the predicted deformed halos in the near-N=50N=50 even-ZZ odd-NN candidates 71^{71}Cr, 73^{73}Cr, 75^{75}Cr, and 77^{77}Fe, and the suggested 53^{53}Ar, are physically realized. A complete answer establishes, for the candidate set: (i) whether each isotope lies inside the neutron drip line, and its actual one-neutron separation energy SnS_n; (ii) whether its ground state is a halo, and if so the halo character — the bandhead spin-parity (the spin-parity of the lowest state of the rotational band) and the Ωπ\Omega^\pi of the valence orbital, the deformation (magnitude and sign, including possible triaxiality), the binding-energy window in which the halo survives under the adopted quantitative halo criterion, and the ss-, pp-, or higher-ll content of the valence wave function; and (iii) the observable consequences — matter-radius enhancement, one-neutron-removal and Coulomb-breakup cross sections with momentum distributions, and low-energy E1 strength — that experimentally confirm or exclude the halo. A solution resolves the task if it determines, for each named candidate, whether it lies inside the neutron drip line, its actual one-neutron separation energy SnS_n, and whether its ground state is a halo; the halo-character detail in (ii) and the observable consequences in (iii) are required only for the candidates thereby established to be halos. These components jointly answer one question, the existence and character of halos beyond 37^{37}Mg; the named candidate set is the operative focus of that question.

References

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